Exploring Systems of Equations

What is the first step in solving a system of linear equations?

• Eliminating a variable

• Graphing the equations

• Adding the equations

• Multiplying both sides by a constant

What does the intersection point of two lines represent in a system of linear equations?

• The point where both lines are parallel

• The solution to the system of equations

• The midpoint of the lines

• The point where both lines are perpendicular

How do you eliminate a variable in a system of equations?

• By rearranging the equations

• By subtracting one equation from the other

• By multiplying one equation by a constant

• By adding the equations directly

What is the solution to the system of equations 9x - 4y = -78 and 4x + y = -18?

• x = -6, y = 6

• x = 6, y = 6

• x = 6, y = -6

• x = -6, y = -6

What is the purpose of multiplying an equation by a constant in the context of solving systems of equations?

• To find the slope of the line

• To make the equations easier to graph

• To eliminate a variable

• To simplify the equation

What is the solution to the system of equations -7x - 4y = 9 and x + 2y = 3?

• x = -3, y = 3

• x = 3, y = 3

• x = 3, y = -3

• x = -3, y = -3

What is the least common multiple used for in solving systems of equations?

• To simplify the equations

• To find the slope of the lines

• To eliminate a variable

• To find the intersection point

What is the solution to the system of equations -3x - 9y = 66 and -7x + 4y = -71?

• x = -5, y = -9

• x = 5, y = -9

• x = 5, y = 9

• x = -5, y = 9

What is the first step in solving the system of equations -3x - 9y = 66 and -7x + 4y = -71?

• Graph the equations

• Multiply the equations by constants

• Add the equations

• Subtract the equations

What is the final step in solving a system of linear equations after finding the value of one variable?

• Multiply the equations by a constant

• Graph the solution

• Substitute the value back into one of the original equations

• Check the solution